Predicting Binary-Interaction Parameters of Cubic Equations of State for Petroleum Fluids Containing Pseudo-components

Abstract

Cubic equations of state (EoS) are widely used for the prediction of thermodynamic properties of petroleum fluids containing both well-defined and <i>pseudo</i>-components. Such EoS require as input parameters the critical temperature (<i>T</i>_c), the critical pressure (<i>P</i>_c), and the acentric factor (ω) of each compound. For well-defined components, such properties are known from experiments and easily obtained. For pseudo-components they are routinely estimated using one of the numerous characterization methods (CM) available in the open literature. A CM is nothing more than a set of correlations which makes it possible to estimate <i>T</i>_c, <i>P</i>_c, and ω of a pseudo-component (PC) from the knowledge of its normal boiling point (NBP), molecular weight (MW), or specific gravity (SG). Regarding the binary-interaction parameters (BIP) <i>k</i>_<i>ij</i> (where <i>i</i> and/or <i>j</i> are/is a pseudo-component(s)) which appear in classical mixing rules, they are either set to zero or estimated by a specific correlation. Most of the proposed correlations are however purely empirical and usually only make possible the estimation of the <i>k</i>_<i>ij</i> between light components (H₂S, CO₂, N₂, C₁, C₂, and C₃) and a pseudo-component. The full <i>k</i>_<i>ij</i> matrix is thus beyond reach and the BIP are usually temperature-independent. In this work, the PPR78 model is used to predict BIP suitable for the Peng–Robinson EoS whereas the PR2SRK model is used to predict BIP suitable for any other cubic EoS. Since these models can be seen as group-contribution methods (GCM) to estimate the <i>k</i>_<i>ij</i>, one needs to access the chemical structure of each PC. The chemical structure of PC is however too complex to be precisely determined. For this reason, it was assumed that each PC was made of only three groups: C_PAR, C_NAP, and C_ARO in order to take into account their paraffinic, naphthenic, and aromatic characters, respectively. The occurrences (<b>N</b>) of the three aforementioned groups are determined from the knowledge of <i>T</i>_c,CM, <i>P</i>_c,CM, and ω_CM (issuing from a CM). To reach this goal, GC methods aimed at estimating <i>T</i>_c, <i>P</i>_c, and ω of hydrocarbons were developed. Such methods have the ability to consider only three elementary groups: C_PAR, C_NAP, and C_ARO. In the end, the three known properties (<i>T</i>_c,CM, <i>P</i>_c,CM, and ω_CM) can be expressed as functions of <i>N</i>_PAR, <i>N</i>_NAP, and <i>N</i>_ARO (the occurrences of the groups) and we thus only need to solve a system of three equations with three unknowns. To check its validity, the present approach is applied to the prediction of the phase behavior of real petroleum fluids containing pseudo-components. The test results show the pertinence of the proposed method to predict the <i>k</i>_<i>ij</i> when <i>i</i> and/or <i>j</i> is a pseudo-component